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11. AREAS RELATED TO CIRCLES

The chapter covers the concepts of sectors and segments of a circle, including the formulas needed to calculate their areas and the lengths of arcs. It provides detailed explanations of how to derive the area of a sector based on its angle and radius, and also discusses the relationship between the areas of segments and their corresponding triangles. Various examples reinforce the application of these concepts in solving problems relevant to circles.

Sections

AREAS RELATED TO CIRCLES

This section discusses the concepts of sectors and segments of circles, detailing their areas and the formulas to calculate them.

11 Section Overview

Start current section content and materials

11.1 Areas of Sector and Segment of a Circle

This section explores the definitions, formulas, and calculations related to the areas of sectors and segments of circles.

11.2 Summary

This section outlines the essential formulas for calculating the length of an arc and the area of a sector and segment of a circle.

Learning Objectives

  • Length of an arc of a sector of a circle with radius r and angle with degree measure θ is θ/360 × 2πr.

  • Area of a sector of a circle with radius r and angle with degree measure θ is θ/360 × πr².

  • Area of a segment of a circle = Area of the corresponding sector - Area of the corresponding triangle.

Key Concepts

Sector

A sector of a circle is a portion enclosed by two radii and the arc between them.

Segment

A segment of a circle is the area enclosed by a chord and the arc connecting the endpoints of the chord.

Arc Length

The distance along the arc connecting two points on the circle, calculable using the arc's angle and radius.

Area of Sector

The area of a sector can be calculated using the formula (θ/360) × πr².

Practice Exercises

Total Questions

5

Estimated Time

10 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting